{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pylab as pl\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "mpl.rcParams['font.sans-serif'] = ['SimHei']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 拟合与优化-optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 非线性方程组求解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.70622057 -0.6        -2.5       ]\n",
      "[0.0, -9.126033262418787e-14, 5.329070518200751e-15]\n"
     ]
    }
   ],
   "source": [
    "from math import sin, cos\n",
    "from scipy import optimize\n",
    "\n",
    "def f(x): #❶\n",
    "    x0, x1, x2 = x.tolist() #❷\n",
    "    return [\n",
    "        5*x1+3,\n",
    "        4*x0*x0 - 2*sin(x1*x2),\n",
    "        x1*x2 - 1.5\n",
    "    ]\n",
    "\n",
    "# f计算方程组的误差，[1,1,1]是未知数的初始值\n",
    "result = optimize.fsolve(f, [1,1,1]) #❸\n",
    "print (result)\n",
    "print (f(result))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.70622057 -0.6        -2.5       ]\n",
      "[0.0, -9.126033262418787e-14, 5.329070518200751e-15]\n"
     ]
    }
   ],
   "source": [
    "def j(x):  #❶\n",
    "    x0, x1, x2 = x.tolist()\n",
    "    return [[0, 5, 0],\n",
    "            [8 * x0, -2 * x2 * cos(x1 * x2), -2 * x1 * cos(x1 * x2)],\n",
    "            [0, x2, x1]]\n",
    "\n",
    "\n",
    "result = optimize.fsolve(f, [1, 1, 1], fprime=j)  #❷\n",
    "print(result)\n",
    "print(f(result))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 最小二乘拟合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k = 0.6134953491930442 b = 1.794092543259387\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import optimize\n",
    "\n",
    "X = np.array([ 8.19,  2.72,  6.39,  8.71,  4.7 ,  2.66,  3.78])\n",
    "Y = np.array([ 7.01,  2.78,  6.47,  6.71,  4.1 ,  4.23,  4.05])\n",
    "\n",
    "def residuals(p): #❶\n",
    "    \"计算以p为参数的直线和原始数据之间的误差\"\n",
    "    k, b = p\n",
    "    return Y - (k*X + b)\n",
    "\n",
    "# leastsq使得residuals()的输出数组的平方和最小，参数的初始值为[1,0]\n",
    "r = optimize.leastsq(residuals, [1, 0]) #❷\n",
    "k, b = r[0]\n",
    "print (\"k =\",k, \"b =\",b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a350dee748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%figonly=最小化正方形面积之和（左），误差曲面（右）\n",
    "scale_k = 1.0\n",
    "scale_b = 10.0\n",
    "scale_error = 1000.0\n",
    "\n",
    "def S(k, b):\n",
    "    \"计算直线y=k*x+b和原始数据X、Y的误差的平方和\"\n",
    "    error = np.zeros(k.shape)\n",
    "    for x, y in zip(X, Y):\n",
    "        error += (y - (k * x + b)) ** 2\n",
    "    return error\n",
    "\n",
    "ks, bs = np.mgrid[k - scale_k:k + scale_k:40j, b - scale_b:b + scale_b:40j]\n",
    "error = S(ks, bs) / scale_error\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib.patches import Rectangle\n",
    "\n",
    "fig = pl.figure(figsize=(12, 5))\n",
    "\n",
    "ax1 = pl.subplot(121)\n",
    "\n",
    "ax1.plot(X, Y, \"o\")\n",
    "X0 = np.linspace(2, 10, 3)\n",
    "Y0 = k*X0 + b\n",
    "ax1.plot(X0, Y0)\n",
    "\n",
    "for x, y in zip(X, Y):\n",
    "    y2 = k*x+b\n",
    "    rect = Rectangle((x,y), abs(y-y2), y2-y, facecolor=\"red\", alpha=0.2)\n",
    "    ax1.add_patch(rect)\n",
    "\n",
    "ax1.set_aspect(\"equal\")\n",
    "\n",
    "\n",
    "ax2 = fig.add_subplot(122, projection='3d')\n",
    "\n",
    "ax2.plot_surface(\n",
    "    ks, bs / scale_b, error, rstride=3, cstride=3, cmap=\"jet\", alpha=0.5)\n",
    "ax2.scatter([k], [b / scale_b], [S(k, b) / scale_error], c=\"r\", s=20)\n",
    "ax2.set_xlabel(\"$k$\")\n",
    "ax2.set_ylabel(\"$b$\")\n",
    "ax2.set_zlabel(\"$error$\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "真实参数: [10, 0.34, 0.5235987755982988]\n",
      "拟合参数 [10.25218748  0.3423992   0.50817423]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a3531df940>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a3530f69e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%fig=带噪声的正弦波拟合\n",
    "def func(x, p):  #❶\n",
    "    \"\"\"\n",
    "    数据拟合所用的函数: A*sin(2*pi*k*x + theta)\n",
    "    \"\"\"\n",
    "    A, k, theta = p\n",
    "    return A * np.sin(2 * np.pi * k * x + theta)\n",
    "\n",
    "\n",
    "def residuals(p, y, x):  #❷\n",
    "    \"\"\"\n",
    "    实验数据x, y和拟合函数之间的差，p为拟合需要找到的系数\n",
    "    \"\"\"\n",
    "    return y - func(x, p)\n",
    "\n",
    "\n",
    "x = np.linspace(0, 2 * np.pi, 100)\n",
    "A, k, theta = 10, 0.34, np.pi / 6  # 真实数据的函数参数\n",
    "y0 = func(x, [A, k, theta])  # 真实数据\n",
    "# 加入噪声之后的实验数据\n",
    "np.random.seed(0)\n",
    "y1 = y0 + 2 * np.random.randn(len(x))  #❸\n",
    "\n",
    "p0 = [7, 0.40, 0]  # 第一次猜测的函数拟合参数\n",
    "\n",
    "# 调用leastsq进行数据拟合\n",
    "# residuals为计算误差的函数\n",
    "# p0为拟合参数的初始值\n",
    "# args为需要拟合的实验数据\n",
    "plsq = optimize.leastsq(residuals, p0, args=(y1, x))  #❹\n",
    "\n",
    "print(u\"真实参数:\", [A, k, theta])\n",
    "print(u\"拟合参数\", plsq[0])  # 实验数据拟合后的参数\n",
    "\n",
    "pl.plot(x, y1, \"o\", label=u\"带噪声的实验数据\")\n",
    "pl.plot(x, y0, label=u\"真实数据\")\n",
    "pl.plot(x, func(x, plsq[0]), label=u\"拟合数据\")\n",
    "pl.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10.25218748  0.3423992   0.50817425]\n"
     ]
    }
   ],
   "source": [
    "def func2(x, A, k, theta):\n",
    "    return A*np.sin(2*np.pi*k*x+theta)   \n",
    "\n",
    "popt, _ = optimize.curve_fit(func2, x, y1, p0=p0)\n",
    "print (popt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "真实参数: [10, 0.34, 0.5235987755982988]\n",
      "拟合参数 [ 0.71093469  1.02074585 -0.12776742]\n"
     ]
    }
   ],
   "source": [
    "popt, _ = optimize.curve_fit(func2, x, y1, p0=[10, 1, 0])\n",
    "\n",
    "print(u\"真实参数:\", [A, k, theta])\n",
    "\n",
    "print(u\"拟合参数\", popt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 计算函数局域最小值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nelder-Mead : min= 5.30934e-10, f count=125, fprime count=  0, fhess count=  0\n",
      "Powell      : min=           0, f count= 52, fprime count=  0, fhess count=  0\n",
      "CG          : min= 9.63056e-21, f count= 39, fprime count= 39, fhess count=  0\n",
      "BFGS        : min= 1.84992e-16, f count= 40, fprime count= 40, fhess count=  0\n",
      "Newton-CG   : min= 5.22666e-10, f count= 60, fprime count= 97, fhess count= 38\n",
      "L-BFGS-B    : min=  6.5215e-15, f count= 33, fprime count= 33, fhess count=  0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:415: RuntimeWarning: Method Nelder-Mead does not use gradient information (jac).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:420: RuntimeWarning: Method Nelder-Mead does not use Hessian information (hess).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:415: RuntimeWarning: Method Powell does not use gradient information (jac).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:420: RuntimeWarning: Method Powell does not use Hessian information (hess).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:420: RuntimeWarning: Method CG does not use Hessian information (hess).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:420: RuntimeWarning: Method BFGS does not use Hessian information (hess).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:420: RuntimeWarning: Method L-BFGS-B does not use Hessian information (hess).\n",
      "  RuntimeWarning)\n"
     ]
    }
   ],
   "source": [
    "def target_function(x, y):\n",
    "    return (1 - x)**2 + 100 * (y - x**2)**2\n",
    "\n",
    "\n",
    "class TargetFunction(object):\n",
    "    def __init__(self):\n",
    "        self.f_points = []\n",
    "        self.fprime_points = []\n",
    "        self.fhess_points = []\n",
    "\n",
    "    def f(self, p):\n",
    "        x, y = p.tolist()\n",
    "        z = target_function(x, y)\n",
    "        self.f_points.append((x, y))\n",
    "        return z\n",
    "\n",
    "    def fprime(self, p):\n",
    "        x, y = p.tolist()\n",
    "        self.fprime_points.append((x, y))\n",
    "        dx = -2 + 2 * x - 400 * x * (y - x**2)\n",
    "        dy = 200 * y - 200 * x**2\n",
    "        return np.array([dx, dy])\n",
    "\n",
    "    def fhess(self, p):\n",
    "        x, y = p.tolist()\n",
    "        self.fhess_points.append((x, y))\n",
    "        return np.array([[2 * (600 * x**2 - 200 * y + 1), -400 * x],\n",
    "                         [-400 * x, 200]])\n",
    "\n",
    "\n",
    "def fmin_demo(method):\n",
    "    target = TargetFunction()\n",
    "    init_point = (-1, -1)\n",
    "    res = optimize.minimize(\n",
    "        target.f,\n",
    "        init_point,\n",
    "        method=method,\n",
    "        jac=target.fprime,\n",
    "        hess=target.fhess)\n",
    "    return res, [\n",
    "        np.array(points) for points in (target.f_points, target.fprime_points,\n",
    "                                        target.fhess_points)\n",
    "    ]\n",
    "\n",
    "\n",
    "methods = (\"Nelder-Mead\", \"Powell\", \"CG\", \"BFGS\", \"Newton-CG\", \"L-BFGS-B\")\n",
    "for method in methods:\n",
    "    res, (f_points, fprime_points, fhess_points) = fmin_demo(method)\n",
    "    print(\n",
    "        \"{:12s}: min={:12g}, f count={:3d}, fprime count={:3d}, fhess count={:3d}\"\n",
    "        .format(method, float(res[\"fun\"]), len(f_points), len(fprime_points),\n",
    "                len(fhess_points)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:415: RuntimeWarning: Method Nelder-Mead does not use gradient information (jac).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:420: RuntimeWarning: Method Nelder-Mead does not use Hessian information (hess).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:415: RuntimeWarning: Method Powell does not use gradient information (jac).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:420: RuntimeWarning: Method Powell does not use Hessian information (hess).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:420: RuntimeWarning: Method CG does not use Hessian information (hess).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:420: RuntimeWarning: Method BFGS does not use Hessian information (hess).\n",
      "  RuntimeWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py:420: RuntimeWarning: Method L-BFGS-B does not use Hessian information (hess).\n",
      "  RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a35316a0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%figonly=各种优化算法的搜索路径\n",
    "def draw_fmin_demo(f_points, fprime_points, ax):\n",
    "    xmin, xmax = -3, 3\n",
    "    ymin, ymax = -3, 3\n",
    "    Y, X = np.ogrid[ymin:ymax:500j,xmin:xmax:500j]\n",
    "    Z = np.log10(target_function(X, Y))\n",
    "    zmin, zmax = np.min(Z), np.max(Z)\n",
    "    ax.imshow(Z, extent=(xmin,xmax,ymin,ymax), origin=\"bottom\", aspect=\"auto\", cmap=\"gray\")\n",
    "    ax.plot(f_points[:,0], f_points[:,1], lw=1)\n",
    "    ax.scatter(f_points[:,0], f_points[:,1], c=range(len(f_points)), s=50, linewidths=0)\n",
    "    if len(fprime_points):\n",
    "        ax.scatter(fprime_points[:, 0], fprime_points[:, 1], marker=\"x\", color=\"w\", alpha=0.5)\n",
    "    ax.set_xlim(xmin, xmax)\n",
    "    ax.set_ylim(ymin, ymax)\n",
    "\n",
    "fig, axes = pl.subplots(2, 3, figsize=(9, 6))\n",
    "methods = (\"Nelder-Mead\", \"Powell\", \"CG\", \"BFGS\", \"Newton-CG\", \"L-BFGS-B\")\n",
    "for ax, method in zip(axes.ravel(), methods):\n",
    "    res, (f_points, fprime_points, fhess_points) = fmin_demo(method)\n",
    "    draw_fmin_demo(f_points, fprime_points, ax)\n",
    "    ax.set_aspect(\"equal\")\n",
    "    ax.set_title(method)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 计算全域最小值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x, p):\n",
    "    A, k, theta = p\n",
    "    return A*np.sin(2*np.pi*k*x+theta)\n",
    "\n",
    "def func_error(p, y, x):\n",
    "    return np.sum((y - func(x, p))**2)   \n",
    "\n",
    "x = np.linspace(0, 2*np.pi, 100)\n",
    "A, k, theta = 10, 0.34, np.pi/6 \n",
    "y0 = func(x, [A, k, theta])\n",
    "np.random.seed(0)\n",
    "y1 = y0 + 2 * np.random.randn(len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10.25218676 -0.34239909  2.63341581]\n"
     ]
    }
   ],
   "source": [
    "result = optimize.basinhopping(func_error, (1, 1, 1),\n",
    "                      niter = 10,\n",
    "                      minimizer_kwargs={\"method\":\"L-BFGS-B\",\n",
    "                                        \"args\":(y1, x)})\n",
    "print (result.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a352e40cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%figonly=用`basinhopping()`拟合正弦波\n",
    "pl.plot(x, y1, \"o\", label=u\"带噪声的实验数据\")\n",
    "pl.plot(x, y0, label=u\"真实数据\")\n",
    "pl.plot(x, func(x, result.x), label=u\"拟合数据\")\n",
    "pl.legend(loc=\"best\");"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
